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Cite Details

M. Dentz, D. M. Tartakovsky, E. Abarca, A. Guadagnini, X. Sanchez-Vila and J. Carrera, "Perturbation analysis of variable density flow in porous media", Submitted to J. Fluid Mech., 2005


Steady-state distributions of water potential and salt concentration in coastal aquifers are typically illustrated by the Henry problem, which consists of a fully coupled system of flow and transport equations. Coupling is caused by the dependence of water density on salt concentration. While the Henry problem often serves as a benchmark for numerical codes, the accuracy of the existing numerical and approximate analytical solutions is hard to gauge. We provide a closed form formulation of the flow problem in terms of salt concentration and use a perturbation expansion in the coupling parameter to solve it analytically. The perturbation procedure results in a recursive set of flow and transport equations and their solutions that effectively decouples the two processes. This decoupling approach can be applied to a range of problems involving variable density fluids and sheds new light on coupled flow and transport mechanisms.

BibTeX Entry

author = {M. Dentz and D. M. Tartakovsky and E. Abarca and A. Guadagnini and X. Sanchez-Vila and J. Carrera},
title = {Perturbation analysis of variable density flow in porous media},
year = {2005},
urlpdf = {http://math.lanl.gov/~dmt/papers/dentz-2005-perturbation.pdf},
journal = {Submitted to J. Fluid Mech.}